Data Analysis- 1
setwd("/Users/subasishdas1/Desktop/twt")
ndata <- read.csv("N_data.csv")
names(ndata)## [1] "YIELD" "C" "Mn" "Si" "P" "S" "Cr" "Ni"
## [9] "Mo" "Cu" "V" "Al" "Sn" "Ti" "Nb" "B"summary(ndata)## YIELD C Mn Si
## Min. :112.5 Min. :0.1700 Min. :1.10 Min. :0.0000
## 1st Qu.:121.5 1st Qu.:0.2500 1st Qu.:1.33 1st Qu.:0.2600
## Median :124.0 Median :0.2600 Median :1.35 Median :0.2700
## Mean :124.2 Mean :0.2561 Mean :1.34 Mean :0.2733
## 3rd Qu.:126.8 3rd Qu.:0.2700 3rd Qu.:1.37 3rd Qu.:0.2900
## Max. :135.7 Max. :0.3000 Max. :1.45 Max. :0.3500
## P S Cr Ni
## Min. :0.0060 Min. :0.001000 Min. :0.0700 Min. :0.080
## 1st Qu.:0.0090 1st Qu.:0.002000 1st Qu.:0.2000 1st Qu.:0.100
## Median :0.0110 Median :0.003000 Median :0.2100 Median :0.107
## Mean :0.0112 Mean :0.003627 Mean :0.2008 Mean :0.107
## 3rd Qu.:0.0120 3rd Qu.:0.005000 3rd Qu.:0.2300 3rd Qu.:0.110
## Max. :0.0200 Max. :0.010000 Max. :0.2800 Max. :0.170
## Mo Cu V Al
## Min. :0.0300 Min. :0.0310 Min. :0.000300 Min. :0.01800
## 1st Qu.:0.2100 1st Qu.:0.2600 1st Qu.:0.005000 1st Qu.:0.02600
## Median :0.2200 Median :0.2800 Median :0.006000 Median :0.03000
## Mean :0.1912 Mean :0.2802 Mean :0.005454 Mean :0.03032
## 3rd Qu.:0.2300 3rd Qu.:0.3000 3rd Qu.:0.007000 3rd Qu.:0.03300
## Max. :0.2500 Max. :0.3500 Max. :0.008000 Max. :0.04800
## Sn Ti Nb B
## Min. :0.01000 Min. :0.02000 Min. :0.000200 Min. :0.002100
## 1st Qu.:0.01300 1st Qu.:0.03400 1st Qu.:0.001000 1st Qu.:0.002700
## Median :0.01500 Median :0.04000 Median :0.004000 Median :0.002900
## Mean :0.01459 Mean :0.04095 Mean :0.003442 Mean :0.002984
## 3rd Qu.:0.01600 3rd Qu.:0.04300 3rd Qu.:0.005000 3rd Qu.:0.003300
## Max. :0.02400 Max. :0.42000 Max. :0.010000 Max. :0.004000Correlation plot
library(corrplot)
corrp <- cor(ndata)
corrplot(corrp, method = "circle")
Data Modeling
Variable selection
library(leaps)
leaps=regsubsets(YIELD ~ ., data=ndata, nbest=10)
plot(leaps, scale="adjr2") 
plot(leaps, scale="bic")
Modeling
null=lm(YIELD ~1, data=ndata)
null##
## Call:
## lm(formula = YIELD ~ 1, data = ndata)
##
## Coefficients:
## (Intercept)
## 124.2full=lm(YIELD ~ ., data=ndata)
full##
## Call:
## lm(formula = YIELD ~ ., data = ndata)
##
## Coefficients:
## (Intercept) C Mn Si P
## 101.5007 33.1241 3.3755 4.2406 66.5251
## S Cr Ni Mo Cu
## -83.8527 7.7444 -3.2322 -16.2950 10.2331
## V Al Sn Ti Nb
## 175.3343 36.7821 -54.0863 0.1583 267.6709
## B
## 1647.1221step(null, scope=list(lower=null, upper=full), direction="forward")## Start: AIC=1256.23
## YIELD ~ 1
##
## Df Sum of Sq RSS AIC
## + B 1 322.43 7224.9 1238.9
## + Nb 1 215.76 7331.5 1245.4
## + C 1 165.04 7382.3 1248.5
## + V 1 147.06 7400.2 1249.5
## + Mn 1 105.28 7442.0 1252.0
## + Cr 1 104.49 7442.8 1252.1
## + Si 1 87.96 7459.3 1253.0
## + Cu 1 83.11 7464.2 1253.3
## + Al 1 41.85 7505.4 1255.8
## <none> 7547.3 1256.2
## + Mo 1 27.87 7519.4 1256.6
## + P 1 24.86 7522.4 1256.8
## + Ti 1 2.62 7544.7 1258.1
## + Ni 1 0.98 7546.3 1258.2
## + Sn 1 0.52 7546.8 1258.2
## + S 1 0.01 7547.3 1258.2
##
## Step: AIC=1238.94
## YIELD ~ B
##
## Df Sum of Sq RSS AIC
## + Nb 1 209.576 7015.3 1227.9
## + V 1 180.632 7044.2 1229.8
## + C 1 52.753 7172.1 1237.7
## + Cu 1 46.953 7177.9 1238.0
## + Mn 1 38.710 7186.2 1238.6
## <none> 7224.9 1238.9
## + Cr 1 31.378 7193.5 1239.0
## + Si 1 19.903 7205.0 1239.7
## + P 1 7.797 7217.1 1240.5
## + Al 1 7.217 7217.6 1240.5
## + Ti 1 3.881 7221.0 1240.7
## + Sn 1 0.366 7224.5 1240.9
## + Mo 1 0.331 7224.5 1240.9
## + S 1 0.049 7224.8 1240.9
## + Ni 1 0.000 7224.9 1240.9
##
## Step: AIC=1227.93
## YIELD ~ B + Nb
##
## Df Sum of Sq RSS AIC
## + C 1 60.514 6954.8 1226.1
## + Cu 1 40.167 6975.1 1227.4
## + Cr 1 32.134 6983.2 1227.9
## <none> 7015.3 1227.9
## + Mn 1 30.480 6984.8 1228.0
## + V 1 20.642 6994.6 1228.6
## + Si 1 11.643 7003.6 1229.2
## + P 1 10.442 7004.8 1229.3
## + Al 1 6.395 7008.9 1229.5
## + S 1 0.950 7014.3 1229.9
## + Mo 1 0.785 7014.5 1229.9
## + Ti 1 0.392 7014.9 1229.9
## + Ni 1 0.372 7014.9 1229.9
## + Sn 1 0.043 7015.2 1229.9
##
## Step: AIC=1226.1
## YIELD ~ B + Nb + C
##
## Df Sum of Sq RSS AIC
## + Mo 1 60.888 6893.9 1224.2
## + Cu 1 37.825 6916.9 1225.7
## <none> 6954.8 1226.1
## + V 1 16.616 6938.2 1227.0
## + P 1 15.961 6938.8 1227.1
## + Sn 1 4.041 6950.7 1227.8
## + Ni 1 3.124 6951.7 1227.9
## + S 1 3.054 6951.7 1227.9
## + Al 1 1.521 6953.3 1228.0
## + Cr 1 1.203 6953.6 1228.0
## + Ti 1 0.436 6954.3 1228.1
## + Si 1 0.192 6954.6 1228.1
## + Mn 1 0.002 6954.8 1228.1
##
## Step: AIC=1224.21
## YIELD ~ B + Nb + C + Mo
##
## Df Sum of Sq RSS AIC
## + Cu 1 38.230 6855.7 1223.8
## <none> 6893.9 1224.2
## + Cr 1 27.710 6866.2 1224.4
## + V 1 18.205 6875.7 1225.0
## + Al 1 15.618 6878.3 1225.2
## + Mn 1 12.793 6881.1 1225.4
## + P 1 11.776 6882.1 1225.5
## + S 1 10.764 6883.1 1225.5
## + Si 1 9.249 6884.6 1225.6
## + Ni 1 7.962 6885.9 1225.7
## + Sn 1 1.458 6892.4 1226.1
## + Ti 1 0.350 6893.5 1226.2
##
## Step: AIC=1223.75
## YIELD ~ B + Nb + C + Mo + Cu
##
## Df Sum of Sq RSS AIC
## <none> 6855.7 1223.8
## + Cr 1 25.2420 6830.4 1224.1
## + V 1 16.8617 6838.8 1224.7
## + Al 1 15.2734 6840.4 1224.8
## + Mn 1 15.1436 6840.5 1224.8
## + S 1 12.2085 6843.4 1225.0
## + P 1 9.5788 6846.1 1225.1
## + Si 1 7.9326 6847.7 1225.2
## + Sn 1 1.6096 6854.0 1225.7
## + Ti 1 0.6457 6855.0 1225.7
## + Ni 1 0.2703 6855.4 1225.7##
## Call:
## lm(formula = YIELD ~ B + Nb + C + Mo + Cu, data = ndata)
##
## Coefficients:
## (Intercept) B Nb C Mo
## 106.324 1764.994 372.187 41.007 -8.615
## Cu
## 8.809step(full, data=ndata, direction="backward")## Start: AIC=1237.97
## YIELD ~ C + Mn + Si + P + S + Cr + Ni + Mo + Cu + V + Al + Sn +
## Ti + Nb + B
##
## Df Sum of Sq RSS AIC
## - Ti 1 0.011 6766.5 1236.0
## - Ni 1 0.559 6767.1 1236.0
## - Si 1 4.475 6771.0 1236.3
## - Sn 1 4.974 6771.5 1236.3
## - Mn 1 5.460 6772.0 1236.3
## - P 1 8.514 6775.0 1236.5
## - S 1 10.331 6776.8 1236.6
## - Cr 1 11.529 6778.0 1236.7
## - Al 1 13.454 6780.0 1236.8
## - V 1 13.829 6780.3 1236.9
## <none> 6766.5 1238.0
## - Cu 1 38.618 6805.1 1238.5
## - C 1 48.221 6814.7 1239.1
## - Nb 1 51.828 6818.3 1239.3
## - Mo 1 106.682 6873.2 1242.9
## - B 1 138.080 6904.6 1244.9
##
## Step: AIC=1235.97
## YIELD ~ C + Mn + Si + P + S + Cr + Ni + Mo + Cu + V + Al + Sn +
## Nb + B
##
## Df Sum of Sq RSS AIC
## - Ni 1 0.564 6767.1 1234.0
## - Si 1 4.514 6771.0 1234.3
## - Sn 1 4.985 6771.5 1234.3
## - Mn 1 5.450 6772.0 1234.3
## - P 1 8.522 6775.0 1234.5
## - S 1 10.431 6777.0 1234.7
## - Cr 1 11.533 6778.1 1234.7
## - V 1 13.880 6780.4 1234.9
## - Al 1 13.922 6780.4 1234.9
## <none> 6766.5 1236.0
## - Cu 1 38.607 6805.1 1236.5
## - C 1 48.569 6815.1 1237.1
## - Nb 1 52.003 6818.5 1237.3
## - Mo 1 106.704 6873.2 1240.9
## - B 1 138.299 6904.8 1242.9
##
## Step: AIC=1234
## YIELD ~ C + Mn + Si + P + S + Cr + Mo + Cu + V + Al + Sn + Nb +
## B
##
## Df Sum of Sq RSS AIC
## - Si 1 4.184 6771.3 1232.3
## - Sn 1 5.339 6772.4 1232.3
## - Mn 1 5.729 6772.8 1232.4
## - P 1 8.037 6775.1 1232.5
## - S 1 10.072 6777.2 1232.7
## - Cr 1 12.447 6779.5 1232.8
## - Al 1 13.359 6780.4 1232.9
## - V 1 13.502 6780.6 1232.9
## <none> 6767.1 1234.0
## - Cu 1 39.937 6807.0 1234.6
## - C 1 51.471 6818.6 1235.3
## - Nb 1 52.489 6819.6 1235.4
## - Mo 1 110.845 6877.9 1239.2
## - B 1 140.245 6907.3 1241.1
##
## Step: AIC=1232.28
## YIELD ~ C + Mn + P + S + Cr + Mo + Cu + V + Al + Sn + Nb + B
##
## Df Sum of Sq RSS AIC
## - Sn 1 4.347 6775.6 1230.6
## - Mn 1 6.249 6777.5 1230.7
## - P 1 8.828 6780.1 1230.8
## - Al 1 12.354 6783.6 1231.1
## - S 1 12.613 6783.9 1231.1
## - Cr 1 13.344 6784.6 1231.2
## - V 1 13.517 6784.8 1231.2
## <none> 6771.3 1232.3
## - Cu 1 39.725 6811.0 1232.9
## - C 1 51.920 6823.2 1233.7
## - Nb 1 54.982 6826.2 1233.8
## - Mo 1 106.661 6877.9 1237.2
## - B 1 151.205 6922.5 1240.0
##
## Step: AIC=1230.56
## YIELD ~ C + Mn + P + S + Cr + Mo + Cu + V + Al + Nb + B
##
## Df Sum of Sq RSS AIC
## - Mn 1 5.470 6781.1 1228.9
## - P 1 7.500 6783.1 1229.0
## - S 1 11.650 6787.3 1229.3
## - Al 1 12.858 6788.5 1229.4
## - Cr 1 13.115 6788.7 1229.4
## - V 1 13.980 6789.6 1229.5
## <none> 6775.6 1230.6
## - Cu 1 35.531 6811.1 1230.9
## - Nb 1 54.196 6829.8 1232.1
## - C 1 55.025 6830.6 1232.1
## - Mo 1 103.120 6878.7 1235.2
## - B 1 150.080 6925.7 1238.2
##
## Step: AIC=1228.92
## YIELD ~ C + P + S + Cr + Mo + Cu + V + Al + Nb + B
##
## Df Sum of Sq RSS AIC
## - P 1 8.472 6789.6 1227.5
## - S 1 10.659 6791.7 1227.6
## - V 1 14.983 6796.1 1227.9
## - Al 1 15.791 6796.9 1228.0
## - Cr 1 16.550 6797.6 1228.0
## <none> 6781.1 1228.9
## - Cu 1 33.829 6814.9 1229.1
## - Nb 1 55.389 6836.5 1230.5
## - C 1 67.037 6848.1 1231.3
## - Mo 1 97.720 6878.8 1233.2
## - B 1 148.598 6929.7 1236.5
##
## Step: AIC=1227.47
## YIELD ~ C + S + Cr + Mo + Cu + V + Al + Nb + B
##
## Df Sum of Sq RSS AIC
## - S 1 8.399 6798.0 1226.0
## - Al 1 13.436 6803.0 1226.3
## - V 1 18.722 6808.3 1226.7
## - Cr 1 19.730 6809.3 1226.8
## <none> 6789.6 1227.5
## - Cu 1 35.399 6825.0 1227.8
## - Nb 1 50.588 6840.1 1228.8
## - C 1 62.981 6852.5 1229.5
## - Mo 1 103.567 6893.1 1232.2
## - B 1 167.999 6957.6 1236.3
##
## Step: AIC=1226.02
## YIELD ~ C + Cr + Mo + Cu + V + Al + Nb + B
##
## Df Sum of Sq RSS AIC
## - Al 1 10.397 6808.4 1224.7
## - V 1 20.987 6818.9 1225.4
## - Cr 1 26.276 6824.2 1225.7
## <none> 6798.0 1226.0
## - Cu 1 33.954 6831.9 1226.2
## - Nb 1 46.247 6844.2 1227.0
## - C 1 54.935 6852.9 1227.6
## - Mo 1 100.551 6898.5 1230.5
## - B 1 176.896 6974.9 1235.4
##
## Step: AIC=1224.69
## YIELD ~ C + Cr + Mo + Cu + V + Nb + B
##
## Df Sum of Sq RSS AIC
## - V 1 22.063 6830.4 1224.1
## - Cr 1 30.443 6838.8 1224.7
## <none> 6808.4 1224.7
## - Cu 1 34.022 6842.4 1224.9
## - Nb 1 45.483 6853.8 1225.6
## - C 1 48.336 6856.7 1225.8
## - Mo 1 92.199 6900.6 1228.6
## - B 1 196.303 7004.7 1235.3
##
## Step: AIC=1224.12
## YIELD ~ C + Cr + Mo + Cu + Nb + B
##
## Df Sum of Sq RSS AIC
## - Cr 1 25.242 6855.7 1223.8
## <none> 6830.4 1224.1
## - Cu 1 35.761 6866.2 1224.4
## - C 1 53.331 6883.7 1225.6
## - Mo 1 84.849 6915.3 1227.6
## - B 1 182.516 7012.9 1233.8
## - Nb 1 205.303 7035.7 1235.2
##
## Step: AIC=1223.75
## YIELD ~ C + Mo + Cu + Nb + B
##
## Df Sum of Sq RSS AIC
## <none> 6855.7 1223.8
## - Cu 1 38.230 6893.9 1224.2
## - Mo 1 61.292 6916.9 1225.7
## - C 1 118.900 6974.6 1229.3
## - B 1 179.096 7034.8 1233.2
## - Nb 1 212.327 7068.0 1235.2##
## Call:
## lm(formula = YIELD ~ C + Mo + Cu + Nb + B, data = ndata)
##
## Coefficients:
## (Intercept) C Mo Cu Nb
## 106.324 41.007 -8.615 8.809 372.187
## B
## 1764.994step(full, data=ndata, direction="both")## Start: AIC=1237.97
## YIELD ~ C + Mn + Si + P + S + Cr + Ni + Mo + Cu + V + Al + Sn +
## Ti + Nb + B
##
## Df Sum of Sq RSS AIC
## - Ti 1 0.011 6766.5 1236.0
## - Ni 1 0.559 6767.1 1236.0
## - Si 1 4.475 6771.0 1236.3
## - Sn 1 4.974 6771.5 1236.3
## - Mn 1 5.460 6772.0 1236.3
## - P 1 8.514 6775.0 1236.5
## - S 1 10.331 6776.8 1236.6
## - Cr 1 11.529 6778.0 1236.7
## - Al 1 13.454 6780.0 1236.8
## - V 1 13.829 6780.3 1236.9
## <none> 6766.5 1238.0
## - Cu 1 38.618 6805.1 1238.5
## - C 1 48.221 6814.7 1239.1
## - Nb 1 51.828 6818.3 1239.3
## - Mo 1 106.682 6873.2 1242.9
## - B 1 138.080 6904.6 1244.9
##
## Step: AIC=1235.97
## YIELD ~ C + Mn + Si + P + S + Cr + Ni + Mo + Cu + V + Al + Sn +
## Nb + B
##
## Df Sum of Sq RSS AIC
## - Ni 1 0.564 6767.1 1234.0
## - Si 1 4.514 6771.0 1234.3
## - Sn 1 4.985 6771.5 1234.3
## - Mn 1 5.450 6772.0 1234.3
## - P 1 8.522 6775.0 1234.5
## - S 1 10.431 6777.0 1234.7
## - Cr 1 11.533 6778.1 1234.7
## - V 1 13.880 6780.4 1234.9
## - Al 1 13.922 6780.4 1234.9
## <none> 6766.5 1236.0
## - Cu 1 38.607 6805.1 1236.5
## - C 1 48.569 6815.1 1237.1
## - Nb 1 52.003 6818.5 1237.3
## + Ti 1 0.011 6766.5 1238.0
## - Mo 1 106.704 6873.2 1240.9
## - B 1 138.299 6904.8 1242.9
##
## Step: AIC=1234
## YIELD ~ C + Mn + Si + P + S + Cr + Mo + Cu + V + Al + Sn + Nb +
## B
##
## Df Sum of Sq RSS AIC
## - Si 1 4.184 6771.3 1232.3
## - Sn 1 5.339 6772.4 1232.3
## - Mn 1 5.729 6772.8 1232.4
## - P 1 8.037 6775.1 1232.5
## - S 1 10.072 6777.2 1232.7
## - Cr 1 12.447 6779.5 1232.8
## - Al 1 13.359 6780.4 1232.9
## - V 1 13.502 6780.6 1232.9
## <none> 6767.1 1234.0
## - Cu 1 39.937 6807.0 1234.6
## - C 1 51.471 6818.6 1235.3
## - Nb 1 52.489 6819.6 1235.4
## + Ni 1 0.564 6766.5 1236.0
## + Ti 1 0.015 6767.1 1236.0
## - Mo 1 110.845 6877.9 1239.2
## - B 1 140.245 6907.3 1241.1
##
## Step: AIC=1232.28
## YIELD ~ C + Mn + P + S + Cr + Mo + Cu + V + Al + Sn + Nb + B
##
## Df Sum of Sq RSS AIC
## - Sn 1 4.347 6775.6 1230.6
## - Mn 1 6.249 6777.5 1230.7
## - P 1 8.828 6780.1 1230.8
## - Al 1 12.354 6783.6 1231.1
## - S 1 12.613 6783.9 1231.1
## - Cr 1 13.344 6784.6 1231.2
## - V 1 13.517 6784.8 1231.2
## <none> 6771.3 1232.3
## - Cu 1 39.725 6811.0 1232.9
## - C 1 51.920 6823.2 1233.7
## - Nb 1 54.982 6826.2 1233.8
## + Si 1 4.184 6767.1 1234.0
## + Ni 1 0.234 6771.0 1234.3
## + Ti 1 0.054 6771.2 1234.3
## - Mo 1 106.661 6877.9 1237.2
## - B 1 151.205 6922.5 1240.0
##
## Step: AIC=1230.56
## YIELD ~ C + Mn + P + S + Cr + Mo + Cu + V + Al + Nb + B
##
## Df Sum of Sq RSS AIC
## - Mn 1 5.470 6781.1 1228.9
## - P 1 7.500 6783.1 1229.0
## - S 1 11.650 6787.3 1229.3
## - Al 1 12.858 6788.5 1229.4
## - Cr 1 13.115 6788.7 1229.4
## - V 1 13.980 6789.6 1229.5
## <none> 6775.6 1230.6
## - Cu 1 35.531 6811.1 1230.9
## - Nb 1 54.196 6829.8 1232.1
## - C 1 55.025 6830.6 1232.1
## + Sn 1 4.347 6771.3 1232.3
## + Si 1 3.192 6772.4 1232.3
## + Ni 1 0.492 6775.1 1232.5
## + Ti 1 0.072 6775.5 1232.6
## - Mo 1 103.120 6878.7 1235.2
## - B 1 150.080 6925.7 1238.2
##
## Step: AIC=1228.92
## YIELD ~ C + P + S + Cr + Mo + Cu + V + Al + Nb + B
##
## Df Sum of Sq RSS AIC
## - P 1 8.472 6789.6 1227.5
## - S 1 10.659 6791.7 1227.6
## - V 1 14.983 6796.1 1227.9
## - Al 1 15.791 6796.9 1228.0
## - Cr 1 16.550 6797.6 1228.0
## <none> 6781.1 1228.9
## - Cu 1 33.829 6814.9 1229.1
## - Nb 1 55.389 6836.5 1230.5
## + Mn 1 5.470 6775.6 1230.6
## + Si 1 3.698 6777.4 1230.7
## + Sn 1 3.568 6777.5 1230.7
## + Ni 1 0.688 6780.4 1230.9
## + Ti 1 0.020 6781.1 1230.9
## - C 1 67.037 6848.1 1231.3
## - Mo 1 97.720 6878.8 1233.2
## - B 1 148.598 6929.7 1236.5
##
## Step: AIC=1227.47
## YIELD ~ C + S + Cr + Mo + Cu + V + Al + Nb + B
##
## Df Sum of Sq RSS AIC
## - S 1 8.399 6798.0 1226.0
## - Al 1 13.436 6803.0 1226.3
## - V 1 18.722 6808.3 1226.7
## - Cr 1 19.730 6809.3 1226.8
## <none> 6789.6 1227.5
## - Cu 1 35.399 6825.0 1227.8
## - Nb 1 50.588 6840.1 1228.8
## + P 1 8.472 6781.1 1228.9
## + Mn 1 6.443 6783.1 1229.0
## + Si 1 4.648 6784.9 1229.2
## + Sn 1 2.264 6787.3 1229.3
## + Ni 1 0.088 6789.5 1229.5
## + Ti 1 0.023 6789.5 1229.5
## - C 1 62.981 6852.5 1229.5
## - Mo 1 103.567 6893.1 1232.2
## - B 1 167.999 6957.6 1236.3
##
## Step: AIC=1226.02
## YIELD ~ C + Cr + Mo + Cu + V + Al + Nb + B
##
## Df Sum of Sq RSS AIC
## - Al 1 10.397 6808.4 1224.7
## - V 1 20.987 6818.9 1225.4
## - Cr 1 26.276 6824.2 1225.7
## <none> 6798.0 1226.0
## - Cu 1 33.954 6831.9 1226.2
## - Nb 1 46.247 6844.2 1227.0
## + S 1 8.399 6789.6 1227.5
## - C 1 54.935 6852.9 1227.6
## + Si 1 6.658 6791.3 1227.6
## + P 1 6.212 6791.7 1227.6
## + Mn 1 5.332 6792.6 1227.7
## + Sn 1 1.861 6796.1 1227.9
## + Ti 1 0.150 6797.8 1228.0
## + Ni 1 0.000 6798.0 1228.0
## - Mo 1 100.551 6898.5 1230.5
## - B 1 176.896 6974.9 1235.4
##
## Step: AIC=1224.69
## YIELD ~ C + Cr + Mo + Cu + V + Nb + B
##
## Df Sum of Sq RSS AIC
## - V 1 22.063 6830.4 1224.1
## - Cr 1 30.443 6838.8 1224.7
## <none> 6808.4 1224.7
## - Cu 1 34.022 6842.4 1224.9
## - Nb 1 45.483 6853.8 1225.6
## - C 1 48.336 6856.7 1225.8
## + Al 1 10.397 6798.0 1226.0
## + Mn 1 7.722 6800.6 1226.2
## + S 1 5.360 6803.0 1226.3
## + Si 1 4.973 6803.4 1226.4
## + P 1 4.774 6803.6 1226.4
## + Sn 1 2.268 6806.1 1226.5
## + Ti 1 0.672 6807.7 1226.7
## + Ni 1 0.194 6808.2 1226.7
## - Mo 1 92.199 6900.6 1228.6
## - B 1 196.303 7004.7 1235.3
##
## Step: AIC=1224.12
## YIELD ~ C + Cr + Mo + Cu + Nb + B
##
## Df Sum of Sq RSS AIC
## - Cr 1 25.242 6855.7 1223.8
## <none> 6830.4 1224.1
## - Cu 1 35.761 6866.2 1224.4
## + V 1 22.063 6808.4 1224.7
## + Al 1 11.473 6818.9 1225.4
## + Mn 1 9.416 6821.0 1225.5
## - C 1 53.331 6883.7 1225.6
## + P 1 7.625 6822.8 1225.6
## + S 1 7.091 6823.3 1225.7
## + Si 1 5.431 6825.0 1225.8
## + Sn 1 2.330 6828.1 1226.0
## + Ti 1 1.074 6829.3 1226.0
## + Ni 1 0.961 6829.5 1226.1
## - Mo 1 84.849 6915.3 1227.6
## - B 1 182.516 7012.9 1233.8
## - Nb 1 205.303 7035.7 1235.2
##
## Step: AIC=1223.75
## YIELD ~ C + Mo + Cu + Nb + B
##
## Df Sum of Sq RSS AIC
## <none> 6855.7 1223.8
## + Cr 1 25.242 6830.4 1224.1
## - Cu 1 38.230 6893.9 1224.2
## + V 1 16.862 6838.8 1224.7
## + Al 1 15.273 6840.4 1224.8
## + Mn 1 15.144 6840.5 1224.8
## + S 1 12.208 6843.4 1225.0
## + P 1 9.579 6846.1 1225.1
## + Si 1 7.933 6847.7 1225.2
## + Sn 1 1.610 6854.0 1225.7
## - Mo 1 61.292 6916.9 1225.7
## + Ti 1 0.646 6855.0 1225.7
## + Ni 1 0.270 6855.4 1225.7
## - C 1 118.900 6974.6 1229.3
## - B 1 179.096 7034.8 1233.2
## - Nb 1 212.327 7068.0 1235.2##
## Call:
## lm(formula = YIELD ~ C + Mo + Cu + Nb + B, data = ndata)
##
## Coefficients:
## (Intercept) C Mo Cu Nb
## 106.324 41.007 -8.615 8.809 372.187
## B
## 1764.994Algorithmic modeling
Important variable selection
library(randomForest)## randomForest 4.6-10
## Type rfNews() to see new features/changes/bug fixes.impvar <- randomForest(YIELD ~ ., data=ndata, ntree=100, keep.forest=FALSE, importance=TRUE)
varImpPlot(impvar)
(VI_F=importance(impvar))## %IncMSE IncNodePurity
## C 8.812596 387.2932
## Mn 7.192387 441.5513
## Si 8.301346 430.8544
## P 7.129819 398.0089
## S 9.778615 498.2708
## Cr 9.536492 470.1373
## Ni 5.576933 277.4827
## Mo 8.920770 445.7995
## Cu 10.947989 530.4988
## V 7.986155 377.2132
## Al 7.829547 353.4999
## Sn 8.004068 391.8693
## Ti 12.534632 784.3276
## Nb 9.619896 446.5981
## B 11.501397 773.2787### rpart
library(rpart)
fit=rpart(YIELD~., ndata)
plot(fit)
text(fit)
SVM Regression
index <- 1:nrow(ndata)
testindex <- sample(index, trunc(length(index)/3))
testset <- ndata[testindex,]
trainset <- ndata[-testindex,]
library(e1071)
svm.model <- svm(YIELD ~ ., data = trainset, cost = 100, gamma = 1)
svm.pred <- predict(svm.model, testset[,-1])
plot(testset$YIELD, svm.pred)
library(e1071)
svm.model <- svm(YIELD ~ ., data = trainset, cost = 100, gamma = 1)
svm.pred <- predict(svm.model, testset[,-1])
plot(testset$YIELD, svm.pred)
####
svm.model <- svm(YIELD ~ Ti+ B+ Cu+ C+V , data = trainset, cost = 100, gamma = 1)
svm.pred <- predict(svm.model, testset[,-1])
plot(testset$YIELD, svm.pred)
###
####
svm.model <- svm(YIELD ~ Ti+ B+ Cu+ Mn+ Cr, data = trainset, cost = 100, gamma = 1)
svm.pred <- predict(svm.model, testset[,-1])
plot(testset$YIELD, svm.pred)
Conducted by: Subasish Das